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Write sec x as a function of sines and cosines (in this case, sec x = 1 / cos x). Then use the division formula to take the first derivative. Take the derivative of the first derivative to get the second derivative. Reminder: the derivative of sin x is cos x; the derivative of cos x is - sin x.
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What is the second derivative of ln(tan(x))?
f'(x) = 1/tan(x) * sec^2(x) where * means multiply and ^ means to the power of. = cot(x) * sec^2(x) f''(x) = f'(cot(x)*sec^2(x) + cot(x)*f'[sec^2(x)] = -csc^2(x)*sec^2(x) + cot(x)*2tan(x)sec^2(x) = sec^2(x) [cot(x)-csc^2(x)] +2tan(x)cot(x) = sec^2(x) [cot(x)-csc^2(x)] +2
What is the derivitive of a sine wave?
Negative cosine f(x) = sin(x) f'(x) = -cos(x)
How far does a car travel when moving 20 mph for 12 second?
(20 mi / hr) x (12 sec) x (5,280 ft / mi) x (1 hr / 3600 sec)= (20 x 12 x 5,280 / 3,600) (mi - sec - ft - hr / hr - mi - sec)= 352 ft
What is 125 feet per second in miles per hour?
(125 ft/sec) x (1 mi / 5280 ft) x (3600 sec / 1 hr) = (125 x 3600 / 5280) (ft - mi - sec / sec - ft - hr) =85.227 mph (rounded)
200 feet over second equals how many miles over hours?
(200 ft/sec) x (1mile / 5280 ft) x (3600 sec / hour) = (200 x 3,600 / 5,280) (ft - mile - sec / sec - ft - hour)= 136.364 miles per hour (rounded)
